MinT - Best Known (90−42, 90, s)-Nets in Base 8

Best Known (90−42, 90, s)-Nets in Base 8

(90−42, 90, 208)-Net over F₈ — Constructive and digital

Digital (48, 90, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 45, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(90−42, 90, 226)-Net over F₈ — Digital

Digital (48, 90, 226)-net over F₈, using

trace code for nets [i] based on digital (3, 45, 113)-net over F₆₄, using
- net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
    - a curve from the manYPoints database [i]

(90−42, 90, 9186)-Net in Base 8 — Upper bound on s

There is no (48, 90, 9187)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1897 813957 618881 556948 640212 857335 546294 644938 433748 533460 575910 051061 642557 514640 > 8⁹⁰ [i]